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This Bachelor thesis illustrates the connection between the technologies Augmented and Virtual Reality and creates an expedient interdependency of the two forms of presentation. For this purpose, an application in the area of interior design has been implemented, where designing a room can be made more intuitive by using Augmented Reality, as it provides a realistic impression of the planned apartment with a Virtual Reality simulation. Based on the relevant knowledge, a project-concept has been drafted and realized by using several development systems. During a series of tests this implementation has been evaluated and subsequently optimized. The result confirms the assumption, that Augmented and Virtual Reality with their strengths can be combined to an evident solution. This thesis is relevant for computer science students as well as for people interested in innovative solutions.

This thesis explores different approaches for the acceleration of raytracing calculations on the graphics processing unit (GPU). For that a voxel grid is used and extended by the linespace data structure. The linespace consists of direction based shafts and stores the objects located in those shafts in a candidate list. Different methods for the sorting and traversal of the linespace are presented and evaluated. The shown methods cannot provide a speed up of the frame rate without resulting in a loss of image quality.

This thesis presents the use of a local linespace data structure, which is designed and implemented on the basis of an existing GPU-based raytra- cer with a global linespace data structure. For each scene object, an N-tree is generated whose nodes each have a linespace. This saves informations about existing geometry in its shafts. A shaft represents a volume between two faces on the outside of the node. This allows a faster skipping of em- pty spaces during raytracing. Identical objects can access already calcula- ted linespaces, which can reduce the memory requirement by up to 94.13% and the initialization time of the datastructure by up to 97.15%. Due to the local access possibilities dynamic scenes can be visualized. An increase in quality can also be observed.

This thesis presents a novel technique in computer graphics to simulate realtime
global illumination using path tracing. Path tracing is done with compute shaders on the graphics card (GPU) to perform rendering in a highly parallelized manner. To improve the overall performance of tracing rays, the Line Space is used as an acceleration data structure in different variations, resulting in better
empty space skipping. The Line Space saves scene information based on a previous voxelization in direction-dependent shafts and is generated and traversed on the GPU. With this procedure, indirect lighting and soft shadows can be computed in a physically correct way. Furthermore, using the Line Space, path tracing can be performed mostly independent of the complexity of the scene geometry with over 100 frames per second, which is truly real-time and much faster than using a comparable voxel grid. The image quality is not affected negatively by this technique and the shadow quality is in most cases much better compared to shadow-mapping.

Physic simulations allow the creation of dynamic scenes on the computer. Computer generated images become lively and find use in movies, games and engineering applications. GPGPU techniques make use of the graphics card to simulate physics. The simulation of dynamic snow is still little researched. The Material Point Method is the first technique which is capable of showing the dynamics andrncharacteristics of snow.
The hybrid use of Lagrangian particles and a regular cartesian grid enables solving of partial differential equations. Therefore articles are transformed to the grid. The grid velocities can then be updated with the calculation of gradients in an FEM-manner (finite element method). Finally grid node velocities are weight back to the particles to move them across the scene. This method is coupled with a constitutive model to cover the dynamic nature of snow. This include collisions and breaking.
This bachelor thesis connects the recent developments in GPGPU techniques of OpenGL with the Material Point Method to efficiently simulate visually compelling, dynamic snow scenes.

Shadows add a level of realism to a rendered image. Furthermore, they support the user of an augmented reality application through the interactions of virtual objects. The reason for this is that shadows make it easier to judge the position and the size of a virtual object. In 1978, Lance Williams published the shadow mapping algorithm with the aim to render a shadow of objects in a virtual scene. This master thesis presents a modified shadow mapping approach that can additionally be used in Augmented/Mixed Reality applications. First of all the standard algorithm ist extended by a PCF-filter. This filter is used to handle the aliasing-problem on the edges of the shadow and also to soften the shadow. Phantom objects are necessary to be able to operate this approach in a Mixed Reality application. These objects simulate the position and the geometry of the real objects for the algorithm. The approach consists of three steps: First the camera image is drawn into the framebuffer. After that a shadow map, of the virtual objects only, is created. When rendering these objects shadow mapping creates the shadows of virtual objects onto other virtual objects and on themselves. Afterwards the phantom objects are rendered. The depth test is performed on the fragment shader. If a fragment lies in a shadowed region it will get the color of the shadow. However, if it is beeing lit its transpareny value will be set to 1 so that it will not be seen. By applying this procedure all shadows from the virtual objects onto the real objects will be drawn. The results show that the approach can be used in real time in Mixed Reality environments. Additionally a comparison with a modified version of a shadow volume algorithm that can also be used for Mixed Reality applications shows that the approach of this master thesis casts a more realistic shadow in a shorter period of time. All in all this approach increases the level of realism in augmented reality applications and it helps the user measure distances and sizes of the virtual objects more easily.